Many devices that employ magnetic fields have heretofore been encumbered by massive solenoids with their equally bulky power supplies. Thus, there has been increasing interest in the application of permanent magnet structures for such uses as electron-beam focusing and biasing fields. The current demand for compact, strong, static magnetic field sources that require no electric power supplies has created needs for permanent magnet structures of unusual form. A number of configurations have been designed and developed for electron beam guidance in millimeter wave microwave tubes of various types; for dc biasing fields in millimeter wave filters, circulators, isolators, striplines; for field sources in NMR (nuclear magnetic resonance) imagers; and so on. Especially promising for such purposes is the configuration based upon the hollow cylindrical flux source (HCFS) principle described by K. Halbach in "Proceedings of the Eighth International Workshop on Rare Earth Cobalt Permanent Magnets", Univ. of Dayton, Dayton, Ohio, 1985 (pp. 123-136). A HCFS, sometimes called a "magic ring", is a cylindrical permanent magnet shell which produces an internal magnetic field that is more or less constant in magnitude. The field is perpendicular to the axis of the cylinder, and furthermore the field strength can be greater than the remanence of the magnetic material from which the ring is made.
The ideal hollow cylindrical flux source (HCFS) is an infinitely long, annular cylindrical shell which produces an intense magnetic field in its interior working space. The direction of the magnetic field in the working space interior is perpendicular to the long axis of the cylinder. The aforementioned Halbach publication discloses a structure with an octagonal cross section which closely approximates the performance and field configuration of an ideal HCFS (which has a circular cross section). In both the ideal and Halbach configurations, no magnetic flux extends to the exterior of the ring structure (except at the ends of a finite cylinder).
The terms HCFS and "magic ring" as used herein encompasses not only the ideal cylindrical structure but also octagonal, sixteen sided, thirty-two-sided and even higher order polygonal-sided structures which approximates the ideal HCFS structure.
Unfortunately, the ideal HCFS structure is theoretically infinitely long. Thus, achievement of the desirable high uniform magnetic field in the interior of the magic ring structure demands that the structure be made extremely long (theoretically infinite). If the structure is not long enough, distortion of the interior fields will result.
Those concerned with the development of high power devices such as wigglers have continually searched for means to create intense uniform magnetic fields in confined spaces with lightweight devices.